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Control of near‐grazing dynamics and discontinuity‐induced bifurcations in piecewise‐smooth dynamical systems
Author(s) -
Misra Sambit,
Dankowicz Harry
Publication year - 2009
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1551
Subject(s) - discontinuity (linguistics) , piecewise , bifurcation , control theory (sociology) , nonlinear system , limit (mathematics) , mathematics , piecewise linear function , limit cycle , harmonic oscillator , mathematical analysis , parameter space , physics , geometry , computer science , control (management) , quantum mechanics , artificial intelligence
This paper develops a rigorous control paradigm for regulating the near‐grazing bifurcation behavior of limit cycles in piecewise‐smooth dynamical systems. In particular, it is shown that a discrete‐in‐time linear feedback correction to a parameter governing a state‐space discontinuity surface can suppress discontinuity‐induced fold bifurcations of limit cycles that achieve near‐tangential intersections with the discontinuity surface. The methodology ensures a persistent branch of limit cycles over an interval of parameter values near the critical condition of tangential contact that is an order of magnitude larger than that in the absence of control. The theoretical treatment is illustrated with a harmonically excited damped harmonic oscillator with a piecewise‐linear spring stiffness as well as with a piecewise‐nonlinear model of a capacitively excited mechanical oscillator. Copyright © 2009 John Wiley & Sons, Ltd.